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ABSTRACT

1Introduction

This paper is about the relationship between the stock market and the un- employment rate. It has three parts. First, I establish that there has been a high correlation between unemployment and the stock market in U.S. data since 1929. I use post-war quarterly data to estimate a bivariate time series model of unemployment and the real value of the stock market and I show that this model remained structurally stable before and after 1979. Second, I compare three simple theoretical models of the economy; a classical model, a Keynesian model and a "Farmerian model", based on a series of recent books and papers (Farmer, 2008, 2009, 2010a,b,c,d, 2011). I evaluate the ability of each of these models to explain the Great Recession of 2008 and I argue that the Farmerian model provides the most plausible explanation of events. Third, I explain why I have advocated (Farmer, December 30th 2008) a policy of asset market intervention to restore full employment rather than a traditional Keynesian policy ofÞscal stimulus. I present some evidence which shows that the Keynesian consumption function has not remained stable in the post-war period and I explain that evidence by showing that increases in government purchases since 1929 have been accompanied by o setting changes in private consumption expenditure. The behavior of household consumption is consistent with the work of Friedman (1957) who showed that consumers respond to permanent income, or wealth, and not to transitory income. My work explains why high unemployment can persist for long periods of time. Although my explanation is rooted in Keynesian ideas, it goes beyondThe General Theory(Keynes, 1936) by providing an original micro- founded explanation for labor market failure. Unlike the new-Keynesian version ofThe General Theory, my explanation of recessions does not rely 1 on the assumption that prices are sticky. 1 The paper is organized as follows. Section 2 presents a brief review of related literature. Sections 3, 4 and 5 present empirical evidence on the rela- tionship between the stock market and unemployment in U.S. data. Section

6 evaluates that evidence in the light of three alternative economic models

classical and Keynesian models. Section 9 provides a short conclusion.

2 Wealth and Unemployment in the Litera-

ture Much recent work in empirical macroeconomics analyzes data that have been detrended with the Hodrick-PrescottÞlter (Hodrick and Prescott, 1997). Be- cause it removes a dierent trend from each series, the HP-Þlter masks an important correlation between wealth and unemployment that operates at low to medium frequencies. In my work, I detrend data by dividing nom- inal consumption and nominal wealth by the money wage. The resulting detrended consumption and wealth series are very persistent and highly cor- related with unemployment. My focus in this paper is on this correlation. Empirical work by Lettau and Ludvigson (2004) found a low-frequency connection between consumption and wealth and, in a recent extension of their earlier work, Lettau and Ludvigson (2011) provide a statistical model of consumption, wealth and labor earnings as non-stationary time series that are cointegrated. In this paper I show that wealth andunemploymenthave a similar representation as non-stationary cointegrated time series and I pro- vide a theory that connects all of these pieces together. The connection between stock market wealth and unemployment was recognized by Phelps (1999) who pointed out that the stock market boom of 1 Galí (2008) provides a good introduction to the new-Keynesian paradigm. 2 the 1990s was accompanied by a reduction in the unemployment rate. Fi- toussi, Jestaz, Phelps, and Zoega (2000) found a similar correlation between the stock market and unemployment for a variety of European countries. Fol- lowing Phelps (1999) and Hoon and Phelps (1992), these authors explained this connection using Phelps' (1994) structuralist model of the natural rate of unemployment. In Phelps' model, expectations of future pro

Þts causeÞrms

to invest in customer relationships and employee training. In contrast, the theory I develop in this paper explains the connection between stock market wealth and unemployment with a model of multiple equilibria. In my work, any unemployment rate can be a steady state equi- librium and changes in aggregate demand have a permanent eect on the equilibrium unemployment rate. 2 In the model I describe in this paper, labor is continuallyÞred and rehired. As a consequence of this simplifying assumption, the price of capital and the value of the stock market are the same variable. In the data (see for example the paper by Gomme, Ravikumar, and Rupert (2011)), they have very dierent time-series properties and the stock price is much more volatile than the price of capital. In the full dynamic version of the model developed in Farmer (2011), unemployment is a state variable of theÞrm, similar to the capital stock. Here, the stock price will dier from the price of capital. It is an open question as to whether the more general model can replicate the volatility of the stock price that we see in the data. 2 My explanation for persistent unemployment is closer to the models of hysteresis de- scribed by Blanchard and Summers (1987, 1986) and Ball (1999) than the structuralist model of Phelps although the theoretical foundation for persistent unemployment in my work is very dierent from the one provided in those papers. Models based on new- Keynesian economics (see Galí and Gertler(1999)), cannot account for persistent unem- ployment. 3

3 Wealth and Aggregate Demand

Tangible assets in the U.S. are held in the form of factories, machines and houses. Factories and machines are equal to roughly three times GDP; resi- dential real estate comprises an additional two times GDP. Figure 1 shows the history of these two components of tangible assets beginning in theÞrst quarter of 1929 and ending in theÞrst quarter of 2011. The stock market variable is the value of the S&P 500 divided by a measure of the money wage. When a nominal series is detrended in this way I will saythatitismeasuredinwageunits. 3

The measure of housing wealth is my

own estimate, constructed as follows. I multiplied Shiller's historical house price index by the U.S. population and I divided it by the money wage. I multiplied the data by population estimate is based on the assumption that the ratio of people to houses was constant. 4 To construct the wealth index reported in Figure 2, I took0072times my housing wealth variable and I added it to00052times the S&P in wage units. These weights were chosen to give a wealth index that is25housing and 3

5stocks, and that has a mean of100over the period from1929through

2011. The proportions of25and35were chosen to match the proportions

of housing to other tangible assets in Federal Reserve Flow of Funds data. 5 3 The use of wage units to detrend data is a novel technique that I developed and explainedinmybookExpectations Employment and PricesFarmer (2010b). The money wage increases because of growth in the real economy and because of inßation. Detrending by the money wage removes both sources of growth and renders nominal series stationary. 4 Robert Shiller's housing data are available quarterly from 1953q1 through 2011. Be- fore that date I interpolated the annual series to provide quarterly estimates from 1929. Shiller's data are available at 'http://www.econ.yale.edu/~shiller/'. 5 I use the S&P as a measure of wealth because it is available back to1929. My empirical work is robust to the use of the measure of household wealth held as stocks reported in the Federal Reserve Flow of Funds data. That measure moves closely with the S&P500 in the post-war period. 4 300
400
500
600
700
800
900
1,000 4,000 8,000

12,000

16,000

20,000

24,000

28,000

32,000

193019401950196019701980199020002010

Value of the US Housing Stock (author's calculation)

The S&P 500 Measured in Wage Units

Housing Wealth and Stock Market Wealth Since 1929

Shaded areas are

NBER Recessions

Housing Wealth

Stock Market Wealth

Figure 1: Housing and the Stock Market

60
70
80
90
100
110
120
1300
5 10 15 20 25
30
35

2930313233343536373839

Wealth (normalized wage units)

Unemployment Rate

Unemployment and Wealth During the Great Depression

Shaded areas are

NBER Recessions

Wealth (author's calculations)

Unemployment

Figure 2: Unemployment and Wealth in the Great Depression 5 400
500
600
700
800
900
1,000 1,100

1,2003

4 5 6 7 8 9 10 11

000102030405060708091011

Estimated Value of the Housing Stock (wage units)

Unemployment Rate

Unemployment and Housing Wealth During the Great Recession

Shaded areas

are recessions

Housing Wealth (author's calculation)

Unemployment

Figure 3: Unemployment and Housing

8,000

12,000

16,000

20,000

24,000

28,000

32,000

36,000

40,0003

4 5 6 7 8 9 10 11

000102030405060708091011

The S&P 500 Measured in Wage Units

Unemployment Rate

Unemployment and the Stock Market

During the Great Recession

Shaded areas

are recessions

S$P 500

Unemployment

Figure 4: Unemployment and the Stock Market

6 I want to draw attention to two episodes: the Great Depression and the Great Recession. Figure 2 plots an index number of the real value of wealth on the left axis against the unemployment rate on the right axis for data during the Great Depression. ThisÞgure shows a strong correlation (the correlation coecient is088) between wealth and unemployment. Figures 3 and 4 illustrate the behavior of wealth and unemployment dur- ing the Great Recession. I have reported housing and stock market wealth separately for this period because the collapse of the real value of residen- tial real estate was an important source of changes in aggregate demand. A popular, and plausible account of these events, is that the collapse in house pricescausedthe recession. The evidence in favor of this proposition is based on timing. The value of residential real estate peaked in the second quarter of 2006 and unemploy- ment began to increase six months later in the fourth quarter of 2006. The stock market moved later, peaking in the third quarter of 2007. In my interpretation of these events, the values of houses, factories and machines is determined by business and consumer con

Þdence. In recent work

(Farmer, 2011) I have shown how an explosive asset price path can persist as an equilibrium. In my view, the house price crash that began in 2006, was triggered by a shift in beliefs. Households lost conÞdence in the sustainability of continued house price increases and the economy shifted from a dynamic equilibrium in which house prices were growing explosively, to a new steady state equilibrium in which house prices are lower and unemployment higher. This new steady state can potentially be sustained for ever. The fall in the value of residential and commercial real estate triggered a secondary collapse inÞnancial assets whose value was collateralized by real estate wealth. The collapse inÞnancial wealth triggered a stock market crash and households sustained a large drop in permanent income. They responded by increasing their savings and reducing consumption demand. The reduction in demand caused businesses to lay oworkers and it triggered 7 a drop in business income that validated the initial collapse in conÞdence. The 2008Þnancial crisis was a self-fulÞlling prophecy.

4 The Stock Market and Unemployment Since

WWII The correlations between wealth and unemployment that I have reported for the Great Depression and the Great Recession are interesting. But a connection between wealth and unemployment that holds only during certain decades is not one that provides a sound basis on which to build an economic theory. We need to investigate more carefully, the connection between wealth and unemployment over a longer time horizon. That is the purpose of this section. 7.6 8.0 8.4 8.8 9.2 9.6 10.0 10.4 10.8

11.20.8

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

556065707580859095000510

Transformed Unemployment Rate

Log of the S&P 500 (wage units)

Unemployment and the Stock Market

Shaded areas are

NBER Recessions

Unemployment Rate (inverted scale)

S&P 500

Figure 5: Unemploymant and the Stock Market Since 1953 I will focus here on the connection between unemployment and the stock market. Although housing was an important factor in the 2008 recession, 8 house price declines did not precede any of the previous ten post-war re- cessions and it was not until the stock market began to decline in October of 2007 that the U.S. moved into recession. Stock price movements, on the other hand, show a stable relationship with unemployment over the entire post-war period. Figure 5 shows the relationship between unemployment and the stock market from 1953q1 through 2011q1. I have taken the logarithm of the S&P500, measured in wage units, and the logarithm of a logistic transfor- mation of the percentage unemployment rate. These transformations lead to new variables that are unbounded above and below. This an important property since there is evidence that the two transformed variables are non- stationary but cointegrated and in order for a series to be non-stationary it must be able to increase or decrease without limit, independently of its current value. dependent p u p u variable Rsq 0.99 Rsq 0.96 p(-1) 1.41 -0.33 1.30 -0.26 (0.09) (0.10) (0.09) (0.05) p(-2) -0.42 0.27 -0.31 0.24 (0.09) (0.10) (0.09) (0.05) u(-1) 0.13 1.50 -0.05 1.57 (0.05) (0.07) (0.11) (0.06) u(-2) -0.11 -0.60 0.07 -0.62 (0.04) (0.07) (0.11) (0.06) c 0.15 0.77 0.06 0.26 (0.22) (0.24) (0.19) (0.11)1979q4--2011q11953q1--1979q3

Table 1: Estimates from a VAR

Table 1 illustrates the results from estimating a bivariate vector autore- gression using(the logarithm of the S&P500 in wage units) and(the loga- 9 rithm of a logistic transformation of the percentage unemployment rate). The left panel of this table reports regression results for the period from 1953q1 through 1979q3 and the right panel reports results from 1979q4 through

2011q1. Standard errors are in parentheses below each point estimate.

I broke the data in 1979q3 because there is evidence that many macroeco- nomic time series behave very dierently before and after this date (Beyer and Farmer, 2003, 2007; Clarida, Galí, and Gertler, 2000; Lubik and Schorfheide,quotesdbs_dbs17.pdfusesText_23